GCSE · Direct & inverse proportion

Proportion with squares, cubes and rootsExam-style questions

Why y ∝ x², y ∝ √x and y ∝ 1/x² all follow the same three-step method — write the equation, find k, use it — and how the power changes the scaling.

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12 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
$y$ is inversely proportional to $x^{2}$

$z$ is directly proportional to $\sqrt{x}$

When $x = 9$ , $y = 4$ and $z = 6$

Find the value of $y$ when $z = 3$

(5 marks)
Level 5 · 5 marksTry it
2
$a$ is directly proportional to the square of $b$ , and $b$ is directly proportional to the square root of $c$ .

When $c = 16$ , $b = 12$ . When $b = 12$ , $a = 36$ .

(a) Find a formula for $a$ in terms of $c$ .

(b) Work out the value of $a$ when $c = 64$ .
Level 5 · 4 marksTry it
3
$a$ is directly proportional to the square of $b$ : when $b = 2$ , $a = 16$ .

$b$ is directly proportional to the cube root of $c$ : when $c = 8$ , $b = 4$ .

Work out the value of $a$ when $c = 27$ .
Level 5 · 4 marksTry it